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   <div id="projectname">Discontinuous Galerkin
   &#160;<span id="projectnumber">0.0.01</span>
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   <div id="projectbrief">Teste</div>
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<a href="_integration_8f90.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a><a class="code" href="class_gaussian_integration.html">00001</a> <span class="keyword">module</span> <a class="code" href="class_gaussian_integration.html">GaussianIntegration</a>
<a name="l00002"></a>00002 
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="keyword">contains</span>
<a name="l00005"></a>00005 
<a name="l00006"></a><a class="code" href="class_gaussian_integration.html#a89b6a93c00542c5eadcf6c86cf547003">00006</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>LinearIntegrationPoints(n) result (pts)
<a name="l00007"></a>00007         <span class="keyword">implicit none</span>
<a name="l00008"></a>00008         <span class="keywordtype">integer</span>, <span class="keywordtype">intent(in)</span> :: n
<a name="l00009"></a>00009 
<a name="l00010"></a>00010         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(n)</span> :: pts
<a name="l00011"></a>00011 
<a name="l00012"></a>00012         <span class="keyword">select</span> <span class="keyword">case</span>(n)
<a name="l00013"></a>00013             <span class="keyword">case</span>(1)
<a name="l00014"></a>00014                 pts=0.0d0
<a name="l00015"></a>00015             <span class="keyword">case</span>(2)
<a name="l00016"></a>00016                 pts(1) = - 0.577350269189626d0
<a name="l00017"></a>00017                 pts(2) =   0.577350269189626d0
<a name="l00018"></a>00018             <span class="keyword">case</span>(3)
<a name="l00019"></a>00019                 pts(1) = - 0.774596669241483d0
<a name="l00020"></a>00020                 pts(2) =   0.0d0
<a name="l00021"></a>00021                 pts(3) =   0.774596669241483d0
<a name="l00022"></a>00022             <span class="keyword">case</span>(4)
<a name="l00023"></a>00023                 pts(1) = - 0.861136311594953d0
<a name="l00024"></a>00024                 pts(2) = - 0.339981043584856d0
<a name="l00025"></a>00025                 pts(3) =   0.339981043584856d0
<a name="l00026"></a>00026                 pts(4) =   0.861136311594953d0
<a name="l00027"></a>00027             <span class="keyword">case</span>(5)
<a name="l00028"></a>00028                 pts(1) = - 0.906179845938664d0
<a name="l00029"></a>00029                 pts(2) = - 0.538469310105683d0
<a name="l00030"></a>00030                 pts(3) =   0.0d0
<a name="l00031"></a>00031                 pts(4) =   0.538469310105683d0
<a name="l00032"></a>00032                 pts(5) =   0.906179845938664d0
<a name="l00033"></a>00033             <span class="keyword">case</span>(6)
<a name="l00034"></a>00034                 pts(1) = - 0.932469514203152d0
<a name="l00035"></a>00035                 pts(2) = - 0.661209386466265d0
<a name="l00036"></a>00036                 pts(3) = - 0.238619186083197d0
<a name="l00037"></a>00037                 pts(4) =   0.238619186083197d0
<a name="l00038"></a>00038                 pts(5) =   0.661209386466265d0
<a name="l00039"></a>00039                 pts(6) =   0.932469514203152d0
<a name="l00040"></a>00040             <span class="keyword">case</span>(7)
<a name="l00041"></a>00041                 pts(1) = - 0.946107912342759d0
<a name="l00042"></a>00042                 pts(2) = - 0.741531185599394d0
<a name="l00043"></a>00043                 pts(3) = - 0.405845151377397d0
<a name="l00044"></a>00044                 pts(4) =   0.0d0
<a name="l00045"></a>00045                 pts(5) =   0.405845151377397d0
<a name="l00046"></a>00046                 pts(6) =   0.741531185599394d0
<a name="l00047"></a>00047                 pts(7) =   0.946107912342759d0
<a name="l00048"></a>00048             <span class="keyword">case</span>(8)
<a name="l00049"></a>00049                 pts(1) = - 0.960289856497536d0
<a name="l00050"></a>00050                 pts(2) = - 0.796666477413627d0
<a name="l00051"></a>00051                 pts(3) = - 0.525532409916329d0
<a name="l00052"></a>00052                 pts(4) = - 0.183434642495650d0
<a name="l00053"></a>00053                 pts(4) =   0.183434642495650d0
<a name="l00054"></a>00054                 pts(3) =   0.525532409916329d0
<a name="l00055"></a>00055                 pts(2) =   0.796666477413627d0
<a name="l00056"></a>00056                 pts(1) =   0.960289856497536d0
<a name="l00057"></a>00057             <span class="keyword">case</span>(9)
<a name="l00058"></a>00058                 pts(1) = - 0.968160239507626d0
<a name="l00059"></a>00059                 pts(2) = - 0.836031107326636d0
<a name="l00060"></a>00060                 pts(3) = - 0.613371432700590d0
<a name="l00061"></a>00061                 pts(4) = - 0.324253423403809d0
<a name="l00062"></a>00062                 pts(5) =   0.0d0
<a name="l00063"></a>00063                 pts(6) =   0.324253423403809d0
<a name="l00064"></a>00064                 pts(7) =   0.613371432700590d0
<a name="l00065"></a>00065                 pts(8) =   0.836031107326636d0
<a name="l00066"></a>00066                 pts(9) =   0.968160239507626d0
<a name="l00067"></a>00067             <span class="keyword">case</span>(10)
<a name="l00068"></a>00068                 pts(1)  = - 0.973906528517172d0
<a name="l00069"></a>00069                 pts(2)  = - 0.865063366688985d0
<a name="l00070"></a>00070                 pts(3)  = - 0.679409568299024d0
<a name="l00071"></a>00071                 pts(4)  = - 0.433395394129247d0
<a name="l00072"></a>00072                 pts(5)  = - 0.148874338981631d0
<a name="l00073"></a>00073                 pts(6)  =   0.148874338981631d0
<a name="l00074"></a>00074                 pts(7)  =   0.433395394129247d0
<a name="l00075"></a>00075                 pts(8)  =   0.679409568299024d0
<a name="l00076"></a>00076                 pts(9)  =   0.865063366688985d0
<a name="l00077"></a>00077                 pts(10) =   0.973906528517172d0
<a name="l00078"></a>00078             <span class="keyword">case</span> default
<a name="l00079"></a>00079                 pts=0.0d0
<a name="l00080"></a>00080         <span class="keyword">end select</span>
<a name="l00081"></a>00081 
<a name="l00082"></a>00082 <span class="keyword">    end function</span>
<a name="l00083"></a>00083 
<a name="l00084"></a>00084 
<a name="l00085"></a><a class="code" href="class_gaussian_integration.html#a10e88a0d0bff89ce04d55295da8fdf97">00085</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>LinearIntegrationWeights(n) result (wgts)
<a name="l00086"></a>00086         <span class="keyword">implicit none</span>
<a name="l00087"></a>00087         <span class="keywordtype">integer</span>, <span class="keywordtype">intent(in)</span> :: n
<a name="l00088"></a>00088 
<a name="l00089"></a>00089         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(n)</span> :: wgts
<a name="l00090"></a>00090 
<a name="l00091"></a>00091         <span class="keyword">select</span> <span class="keyword">case</span>(n)
<a name="l00092"></a>00092             <span class="keyword">case</span>(1)
<a name="l00093"></a>00093                 wgts    = 2.0d0
<a name="l00094"></a>00094             <span class="keyword">case</span>(2)
<a name="l00095"></a>00095                 wgts(1) = 1.0d0
<a name="l00096"></a>00096                 wgts(2) = 1.0d0
<a name="l00097"></a>00097             <span class="keyword">case</span>(3)
<a name="l00098"></a>00098                 wgts(1) = 0.555555555555555d0
<a name="l00099"></a>00099                 wgts(2) = 0.888888888888888d0
<a name="l00100"></a>00100                 wgts(3) = 0.555555555555555d0
<a name="l00101"></a>00101             <span class="keyword">case</span>(4)
<a name="l00102"></a>00102                 wgts(1) = 0.347854845137454d0
<a name="l00103"></a>00103                 wgts(2) = 0.652145154862546d0
<a name="l00104"></a>00104                 wgts(3) = 0.652145154862546d0
<a name="l00105"></a>00105                 wgts(4) = 0.347854845137454d0
<a name="l00106"></a>00106             <span class="keyword">case</span>(5)
<a name="l00107"></a>00107                 wgts(1) = 0.236926885056189d0
<a name="l00108"></a>00108                 wgts(2) = 0.478628670499366d0
<a name="l00109"></a>00109                 wgts(3) = 0.568888888888889d0
<a name="l00110"></a>00110                 wgts(4) = 0.478628670499366d0
<a name="l00111"></a>00111                 wgts(5) = 0.236926885056189d0
<a name="l00112"></a>00112             <span class="keyword">case</span>(6)
<a name="l00113"></a>00113                 wgts(1) = 0.171324492379170d0
<a name="l00114"></a>00114                 wgts(2) = 0.360761573048139d0
<a name="l00115"></a>00115                 wgts(3) = 0.467913934572691d0
<a name="l00116"></a>00116                 wgts(4) = 0.467913934572691d0
<a name="l00117"></a>00117                 wgts(5) = 0.360761573048139d0
<a name="l00118"></a>00118                 wgts(6) = 0.171324492379170d0
<a name="l00119"></a>00119             <span class="keyword">case</span>(7)
<a name="l00120"></a>00120                 wgts(1) = 0.129484966168870d0
<a name="l00121"></a>00121                 wgts(2) = 0.279705391489277d0
<a name="l00122"></a>00122                 wgts(3) = 0.381830050505119d0
<a name="l00123"></a>00123                 wgts(4) = 0.417959183673469d0
<a name="l00124"></a>00124                 wgts(5) = 0.381830050505119d0
<a name="l00125"></a>00125                 wgts(6) = 0.279705391489277d0
<a name="l00126"></a>00126                 wgts(7) = 0.129484966168870d0
<a name="l00127"></a>00127             <span class="keyword">case</span>(8)
<a name="l00128"></a>00128                 wgts(1) = 0.101228536290376d0
<a name="l00129"></a>00129                 wgts(2) = 0.222381034453374d0
<a name="l00130"></a>00130                 wgts(3) = 0.313706645877887d0
<a name="l00131"></a>00131                 wgts(4) = 0.362683783378362d0
<a name="l00132"></a>00132                 wgts(4) = 0.362683783378362d0
<a name="l00133"></a>00133                 wgts(3) = 0.313706645877887d0
<a name="l00134"></a>00134                 wgts(2) = 0.222381034453374d0
<a name="l00135"></a>00135                 wgts(1) = 0.101228536290376d0
<a name="l00136"></a>00136             <span class="keyword">case</span>(9)
<a name="l00137"></a>00137                 wgts(1) = 0.081274388361574d0
<a name="l00138"></a>00138                 wgts(2) = 0.180648160694857d0
<a name="l00139"></a>00139                 wgts(3) = 0.260610696402935d0
<a name="l00140"></a>00140                 wgts(4) = 0.312347077040003d0
<a name="l00141"></a>00141                 wgts(5) = 0.330239355001260d0
<a name="l00142"></a>00142                 wgts(6) = 0.312347077040003d0
<a name="l00143"></a>00143                 wgts(7) = 0.260610696402935d0
<a name="l00144"></a>00144                 wgts(8) = 0.180648160694857d0
<a name="l00145"></a>00145                 wgts(9) = 0.081274388361574d0
<a name="l00146"></a>00146             <span class="keyword">case</span>(10)
<a name="l00147"></a>00147                 wgts(1)  = 0.066671344308688d0
<a name="l00148"></a>00148                 wgts(2)  = 0.149451349150581d0
<a name="l00149"></a>00149                 wgts(3)  = 0.219086362515982d0
<a name="l00150"></a>00150                 wgts(4)  = 0.269266719309996d0
<a name="l00151"></a>00151                 wgts(5)  = 0.295524224714753d0
<a name="l00152"></a>00152                 wgts(6)  = 0.295524224714753d0
<a name="l00153"></a>00153                 wgts(7)  = 0.269266719309996d0
<a name="l00154"></a>00154                 wgts(8)  = 0.219086362515982d0
<a name="l00155"></a>00155                 wgts(9)  = 0.149451349150581d0
<a name="l00156"></a>00156                 wgts(10) = 0.066671344308688d0
<a name="l00157"></a>00157             <span class="keyword">case</span> default
<a name="l00158"></a>00158                 wgts=0.0d0
<a name="l00159"></a>00159         <span class="keyword">end select</span>
<a name="l00160"></a>00160 
<a name="l00161"></a>00161 <span class="keyword">    end function</span>
<a name="l00162"></a>00162 
<a name="l00163"></a>00163 
<a name="l00164"></a><a class="code" href="class_gaussian_integration.html#a6d6b11c942a8221ecd1f3357237bc359">00164</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>TriangularNIntegrationPoints(m) result (n)
<a name="l00165"></a>00165         <span class="keyword">implicit none</span>
<a name="l00166"></a>00166         <span class="keywordtype">integer</span>, <span class="keywordtype">intent(in)</span> :: m
<a name="l00167"></a>00167         <span class="keywordtype">integer</span> :: n
<a name="l00168"></a>00168 
<a name="l00169"></a>00169         <span class="keyword">select</span> <span class="keyword">case</span>(m)
<a name="l00170"></a>00170             <span class="keyword">case</span>(1)
<a name="l00171"></a>00171                 n = 1
<a name="l00172"></a>00172             <span class="keyword">case</span>(2)
<a name="l00173"></a>00173                 n = 3
<a name="l00174"></a>00174             <span class="keyword">case</span>(3)
<a name="l00175"></a>00175                 n = 4
<a name="l00176"></a>00176             <span class="keyword">case</span>(7)
<a name="l00177"></a>00177                 n = 7
<a name="l00178"></a>00178             <span class="keyword">case</span> default
<a name="l00179"></a>00179                 n = 1
<a name="l00180"></a>00180         <span class="keyword">end select</span>
<a name="l00181"></a>00181 <span class="keyword">    end function</span>
<a name="l00182"></a>00182 
<a name="l00183"></a>00183 
<a name="l00184"></a>00184 
<a name="l00185"></a><a class="code" href="class_gaussian_integration.html#a2b8542cbdd2ef02ae9706c2642f72408">00185</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>TriangularIntegrationPoints(n) result (pts)
<a name="l00186"></a>00186         <span class="keyword">implicit none</span>
<a name="l00187"></a>00187         <span class="keywordtype">integer</span>, <span class="keywordtype">intent(in)</span> :: n
<a name="l00188"></a>00188 
<a name="l00189"></a>00189         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(n,3)</span> :: pts
<a name="l00190"></a>00190 
<a name="l00191"></a>00191         <span class="keyword">select</span> <span class="keyword">case</span>(n)
<a name="l00192"></a>00192             <span class="keyword">case</span>(1)
<a name="l00193"></a>00193                 pts = 1.0d0/3.0d0
<a name="l00194"></a>00194             <span class="keyword">case</span>(3)
<a name="l00195"></a>00195                 pts(1,:)   = 0.5d0
<a name="l00196"></a>00196                 pts(2,1)   = 0.0d0
<a name="l00197"></a>00197                 pts(2,2:3) = 0.5d0
<a name="l00198"></a>00198                 pts(3,1)   = 0.5d0
<a name="l00199"></a>00199                 pts(3,2)   = 0.0d0
<a name="l00200"></a>00200                 pts(3,3)   = 0.5d0
<a name="l00201"></a>00201             <span class="keyword">case</span>(4)
<a name="l00202"></a>00202                 pts(1,:)   = 1.0d0/3.0d0
<a name="l00203"></a>00203                 pts(2,1)   = 0.6d0
<a name="l00204"></a>00204                 pts(2,2:3) = 0.2d0
<a name="l00205"></a>00205                 pts(3,1)   = 0.2d0
<a name="l00206"></a>00206                 pts(3,2)   = 0.6d0
<a name="l00207"></a>00207                 pts(3,3)   = 0.2d0
<a name="l00208"></a>00208                 pts(4,1:2) = 0.2d0
<a name="l00209"></a>00209                 pts(4,3)   = 0.6d0
<a name="l00210"></a>00210             <span class="keyword">case</span>(7)
<a name="l00211"></a>00211                 pts(1,:)   = 1.0d0/3.0d0
<a name="l00212"></a>00212                 pts(2,1)   = 0.0597158717d0
<a name="l00213"></a>00213                 pts(2,2:3) = 0.4701420641d0
<a name="l00214"></a>00214                 pts(3,1)   = 0.4701420641d0
<a name="l00215"></a>00215                 pts(3,2)   = 0.0597158717d0
<a name="l00216"></a>00216                 pts(3,3)   = 0.4701420641d0
<a name="l00217"></a>00217                 pts(4,1:2) = 0.4701420641d0
<a name="l00218"></a>00218                 pts(4,3)   = 0.0597158717d0
<a name="l00219"></a>00219                 pts(5,1)   = 0.7974269853d0
<a name="l00220"></a>00220                 pts(5,2:3) = 0.1012865073d0
<a name="l00221"></a>00221                 pts(6,1)   = 0.1012865073d0
<a name="l00222"></a>00222                 pts(6,2)   = 0.7974269853d0
<a name="l00223"></a>00223                 pts(6,3)   = 0.1012865073d0
<a name="l00224"></a>00224                 pts(7,1:2) = 0.1012865073d0
<a name="l00225"></a>00225                 pts(7,3)   = 0.7974269853d0
<a name="l00226"></a>00226             <span class="keyword">case</span> default
<a name="l00227"></a>00227                 pts = 1.0d0/3.0d0
<a name="l00228"></a>00228         <span class="keyword">end select</span>
<a name="l00229"></a>00229 
<a name="l00230"></a>00230 <span class="keyword">    end function</span>
<a name="l00231"></a>00231 
<a name="l00232"></a>00232 
<a name="l00233"></a>00233 
<a name="l00234"></a><a class="code" href="class_gaussian_integration.html#a94caaff25def1427a3118bc715f43f10">00234</a>     <span class="keywordtype">pure</span> <span class="keyword">function </span>TriangularIntegrationWeights(n) result (wgts)
<a name="l00235"></a>00235         <span class="keyword">implicit none</span>
<a name="l00236"></a>00236         <span class="keywordtype">integer</span>, <span class="keywordtype">intent(in)</span> :: n
<a name="l00237"></a>00237 
<a name="l00238"></a>00238         <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(n)</span> :: wgts
<a name="l00239"></a>00239 
<a name="l00240"></a>00240         <span class="keyword">select</span> <span class="keyword">case</span>(n)
<a name="l00241"></a>00241             <span class="keyword">case</span>(1)
<a name="l00242"></a>00242                 wgts = 1.0d0
<a name="l00243"></a>00243             <span class="keyword">case</span>(3)
<a name="l00244"></a>00244                 wgts(1) = 1.0d0/3.0d0
<a name="l00245"></a>00245                 wgts(2) = 1.0d0/3.0d0
<a name="l00246"></a>00246                 wgts(3) = 1.0d0/3.0d0
<a name="l00247"></a>00247             <span class="keyword">case</span>(4)
<a name="l00248"></a>00248                 wgts(1)   = -27.0d0/48.0d0
<a name="l00249"></a>00249                 wgts(2:4) =  25.0d0/48.0d0
<a name="l00250"></a>00250             <span class="keyword">case</span>(7)
<a name="l00251"></a>00251                 wgts(1)   = 0.225d0
<a name="l00252"></a>00252                 wgts(2:4) = 0.1323941527d0
<a name="l00253"></a>00253                 wgts(5:7) = 0.1259391805d0
<a name="l00254"></a>00254             <span class="keyword">case</span> default
<a name="l00255"></a>00255                 wgts=1.0d0
<a name="l00256"></a>00256         <span class="keyword">end select</span>
<a name="l00257"></a>00257 
<a name="l00258"></a>00258 <span class="keyword">    end function</span>
<a name="l00259"></a>00259 
<a name="l00260"></a>00260 
<a name="l00261"></a><a class="code" href="class_gaussian_integration.html#a77671cc8bda0ad85e3e882bc7ca5d212">00261</a>         <span class="keywordtype">pure</span> <span class="keyword">function </span>GaussianQuadratureIntegral(integrationFunction, IntegrationPoints, IntegrationWeights) result (v)
<a name="l00262"></a>00262                 <span class="keyword">implicit none</span>
<a name="l00263"></a>00263                 <span class="keyword">interface</span>
<a name="l00264"></a>00264                         <span class="keywordtype">pure</span> <span class="keyword">function </span>integrationFunction(eta) result (v)
<a name="l00265"></a>00265                                 <span class="keyword">implicit none</span>
<a name="l00266"></a>00266                                 <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(:)</span>, <span class="keywordtype">intent(in)</span> :: eta
<a name="l00267"></a>00267                                 <span class="keywordtype">real(kind=8)</span> :: v
<a name="l00268"></a>00268 <span class="keyword">                        end function</span>
<a name="l00269"></a>00269 <span class="keyword">                end interface</span>
<a name="l00270"></a>00270                 <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(:,:)</span>, <span class="keywordtype">intent(in)</span> :: IntegrationPoints
<a name="l00271"></a>00271                 <span class="keywordtype">real(kind=8)</span>, <span class="keywordtype">dimension(:)</span>, <span class="keywordtype">intent(in)</span> :: IntegrationWeights
<a name="l00272"></a>00272 
<a name="l00273"></a>00273                 <span class="keywordtype">real(kind=8)</span> :: v
<a name="l00274"></a>00274 
<a name="l00275"></a>00275                 <span class="keywordtype">integer</span> :: nPoints, i
<a name="l00276"></a>00276 
<a name="l00277"></a>00277                 nPoints = <span class="keyword">size</span>(IntegrationPoints, 1)
<a name="l00278"></a>00278                 v = 0.0d0
<a name="l00279"></a>00279                 <span class="keyword">if</span>(<span class="keyword">size</span>(IntegrationWeights) /= nPoints ) return
<a name="l00280"></a>00280 
<a name="l00281"></a>00281                 <span class="keyword">do</span> i = 1, nPoints
<a name="l00282"></a>00282                         v = v + integrationFunction(IntegrationPoints(i,:)) * IntegrationWeights(i)
<a name="l00283"></a>00283                 <span class="keyword">end do</span>
<a name="l00284"></a>00284 <span class="keyword">        end function</span>
<a name="l00285"></a>00285 <span class="keyword">end module</span>
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